Question: Daniel is 2 times as old as Ishaan. 42 years ago, Daniel was 9 times as old as Ishaan. How old is Daniel now?
Explanation: We can use the given information to write down two equations that describe the ages of Daniel and Ishaan. Let Daniel's current age be $d$ and Ishaan's current age be $i$ The information in the first sentence can be expressed in the following equation: $d = 2i$ 42 years ago, Daniel was $d - 42$ years old, and Ishaan was $i - 42$ years old. The information in the second sentence can be expressed in the following equation: $d - 42 = 9(i - 42)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $d$ , it might be easiest to solve our first equation for $i$ and substitute it into our second equation. Solving our first equation for $i$ , we get: $i = d / 2$ . Substituting this into our second equation, we get: $d - 42 = 9($ $(d / 2)$ $- 42)$ which combines the information about $d$ from both of our original equations. Simplifying the right side of this equation, we get: $d - 42 = \dfrac{9}{2} d - 378$ Solving for $d$ , we get: $\dfrac{7}{2} d = 336$ $d = \dfrac{2}{7} \cdot 336 = 96$.